12.2.1: Wind axes-Local horizon orientation
- Page ID
- 78409
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To situate the wind axis reference frame with respect to the local horizon reference frame, the general form given in Example (12.2) is particularized for:
- \(F_I \equiv F_h; F_F \equiv F_w,\)
- \(\delta_3 \equiv \chi \to \text{Yaw angle,}\)
- \(\delta_2 \equiv \gamma \to \text{Flight path angle,}\)
- \(\delta_1 = \equiv \mu \to \text{Bank angle}.\)
The transformation matrix will be:
\[L_{wh} = \begin{bmatrix} \cos \gamma \cos \chi & \cos \gamma \sin \chi & - \sin \gamma \\ \sin \mu \sin \gamma \cos \chi - \cos \mu \sin \chi & \sin \mu \sin \gamma \sin \chi + \cos \mu \cos \chi & \sin \mu \cos \gamma \\ \cos \mu \sin \gamma \cos \chi + \sin \mu \sin \chi & \cos \mu \sin \gamma \sin \chi - \sin \mu \cos \chi & \cos \mu \cos \gamma \end{bmatrix}.\]